OFFSET
1,1
COMMENTS
P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k-1) or k*((3*k-1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k-1)/2 prime] or [k/2 prime and 3*k-1 prime].
LINKS
Eric Weisstein's World of Mathematics, Pentagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
FORMULA
EXAMPLE
a(1) = 12 because P(12) = A000326(12) = 12*(3*12-1)/2 = 210 = 2 * 3 * 5 * 7 is a 4-almost prime (In fact the primorial 4#).
a(3) = 16 because P(16) = 16*(3*16-1)/2 = 376 = 2^3 * 47 is a 4-almost
prime (the prime factors need not be distinct).
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 14 2006
EXTENSIONS
82 inserted by R. J. Mathar, Dec 22 2010
STATUS
approved